Let us take an illustration and suppose that a sum of Rs.1,000 is invested for two years at an annual rate of interest of 8%. What is the future value of this sum based on the following compounding frequencies?

Annual compounding

Semi-annual compounding

Monthly compounding

With annual compounding, t = 2, r = 8% and PV = Rs.1,000.

With semi-annual compounding, t = 4, r = 4% and PV = Rs.1,000. The time frame is now 4 semi-annual periods, and the rate of interest is 4% per semi-annual period.

You may feel that this difference is not much but when you consider longer periods of time like 15 to 20 years, they can make a substantial difference to your wealth.

Let us take an illustration and suppose that a sum of Rs.1,000 is invested for two years at an annual rate of interest of 8%. What is the future value of this sum based on the following compounding frequencies?

Annual compounding

Semi-annual compounding

Monthly compounding

With annual compounding, t = 2, r = 8% and PV = Rs.1,000.

FVt = PV*(1+r)^t FV2 = 1,000*(1+.08)^2 FV2 = 1,000*(1.16640) FV2 = Rs.1,166.40

With semi-annual compounding, t = 4, r = 4% and PV = Rs.1,000. The time frame is now 4 semi-annual periods, and the rate of interest is 4% per semi-annual period.

FVt = PV*(1+r)^t FV4 = 1,000*(1+.04)^4 FV4 = 1,000*(1.16986) FV4 = Rs.1,169.86

With monthly compounding, t = 24, r = 0.6667% and PV = Rs.1,000.

FVt = PV*(1+r)^t FV24 = 1,000*(1+.006667)^24 FV24 = 1,000*(1.17289) FV24 = Rs.1,172.89

You may feel that this difference is not much but when you consider longer periods of time like 15 to 20 years, they can make a substantial difference to your wealth.